## Objectives

- To study the frequency response of RC circuits.
- To determine the frequency response using time domain time domain measurements.
- To study different types of filters (low pass, high pass, band pass and band reject).

## Equipment

- Breadboard
- Function generator
- Oscilloscope
- Digital multimeter (DMM)

## Background

The frequency response of a circuit is a measure of the output in comparison to the input, as a function of frequency. The function used to characterize this is the transfer function, with its It magnitude or gain, typically expressed in dB, and the phase shift, expressed in radians or degrees. The frequency response is important in the analysis and design of filters, tuners, amplifiers, etc.

A filter is a network designed to pass signals with a specific frequency range (passband) and reject or attenuate signals whose frequencies lie outside of this passband. The most common filters are low pass filters, Figure 9 – 1 (a), which pass low frequencies and reject high frequencies, high pass filters, Figure 9 – 1 (b), which pass high frequencies and reject low frequencies, bandpass filters Figure 9 – 1 (c), which pass a select band of frequencies and reject those outside this range and band reject filters, Figure 9 – 1 (d), which reject a specific band of frequencies and pass all other frequencies.

**Figure 9 – 1 Basic types of filters. (a) low pass filter, (b) high pass filter, (c) band pass filter, and (d) band reject filter.**

## Preparation

For circuits (a) and (b) in Figure 9 – 2, R = 1 kΩ, C = 0.1 μF. For circuit (c) in Figure 9 – 2, R_{1} = 1 kΩ, R_{2} = 10 kΩ, C_{1} = 0.01 μF, C_{2} = 0.0056 μF.

- Derive the transfer function.
- Plot or sketch the magnitude vs. frequency and the phase vs. frequency curves in a linear or log scale.
- Indicate if the circuit is a low pass, high pass, band pass or band reject filter.

## Simulation

- In Multisim, build and simulate the circuits (a) through (c) in Figure 9 – 2. Find the frequency response for each circuit. This can be accomplished indirectly. Set the input voltage magnitude to 5 V (pk-to-pk of 10 V). Vary the frequency of the input voltage source from 100 Hz to 100 kHz, record the output voltage magnitude and the phase difference between the input and the output voltages at each frequency. At least 10 or more points are needed in order to completely describe the frequency response. Plot the voltage vs. frequency curve and the phase vs. frequency curve in either linear or log scale. Compare the results of circuit (a) and (b) with those from PREPARATION.
- Specify whether it’s a low pass, high pass or band pass filter for the frequency response curves obtained above.

**Figure 9 – 2 Circuits**

## Experiment

- On breadboard, build circuit (a) in Figure 9 – 2. Connect Ch1 to input and Ch2 to output so that both the input and the output are displayed on the oscilloscope.
- Set the input voltage to . Vary the frequency from 100 Hz to 100 kHz. Refer to SIMULATION for frequency response measurement. Plot the voltage vs. frequency curve and the phase vs. frequency curve in either linear or log scale by selecting at least ten frequency values and determining the amplitude and phase from the oscilloscope.
- Compare the result with that from PREPARATION and/or SIMULATION. What kind of filter is it?
- Repeat step 1 to 3 for circuit (b) and (c).

## Report

Prepare your report as per the guidelines given in APPENDIX III.